Oleg Teryaev JINR, Dubna Single Spin Asymmetries and Duality Diffraction-08, La Londe-les-Maures, September 12, 2008 Oleg Teryaev JINR, Dubna

Outline Duality (between QCD factorization mechanisms) Single Spin Asymmetries in QCD - Sources of (I)FSI 3 ways from Sivers to Twist 3; 3rd way – justifying “ Torino recipe” (talk of M. Anselmino) Non-universality of Sivers function: Colour correlations Sivers function and time-like formfactors Duality in exclusive 2photon processes Conclusions and Outlook

Duality in QCD Quark - hadron (soliton …) Various factorization mechanisms (“quark-quark” duality; “matching”,…) Cf “Hadron-hadron” duality – talks of L. Jenkovszky, V. Magas Single Spin Asymmetries: Sivers function and twist 3 correlations

Single Spin Asymmetries Main properties: – Parity: transverse polarization – Imaginary phase – can be seen from T-invariance or technically - from the imaginary i in the (quark) density matrix Various mechanisms – various sources of phases

Phases in QCD QCD factorization – soft and hard parts- Phases form soft, hard and overlap Assume (generalized) optical theorem – phase due to on-shell intermediate states – positive kinematic variable (= their invariant mass) Hard: Perturbative (a la QED: Barut, Fronsdal (1960): Kane, Pumplin, Repko (78) Efremov (78)

Perturbative PHASES IN QCD

Short+ large overlap– twist 3 Quarks – only from hadrons Various options for factorization – shift of SH separation (prototype of duality) New option for SSA: Instead of 1-loop twist 2 – Born twist 3: Efremov, OT (85, Ferminonc poles); Qiu, Sterman (91, GLUONIC poles)

Twist 3 correlators

Phases in QCD-Large distances in distributions Distributions: Sivers, Boer and Mulders – no positive kinematic variable producing phase QCD: Emerge only due to (initial of final state) interaction between hard and soft parts of the process Brodsky -Hwang-Schmidt model:the same SH interactions as twist 3 but non-suppressed by Q: Sivers function – leading (twist 2). Are they related?

3 ways from Sivers to twist 3 Twist 3 DY - “Effective” or “non-universal” T-odd quark distribution from GP (Boer, Mulders, OT, 97) Moment of SF – GP (Boer, Mulders, Pijlman, 03) Way from large to small kT(outside of applicability region )- Explicit calculation of SIDVCS for Q >> PT (OT, TRANSVERSITY-05) - compensation of 1/Q suppression by GP) Ways from two sides - Matching of perturbative SF and twist 3 for DY, SIDIS +… (Ji,Qiu,Vogelsang,Yuan, 06; Bachetta, Boer, Diehl,Mulders,08) Ways from small to large\ pT - SF at large PT (Ratcliffe, OT, 07)-proof of Torino GPM (talks of M. Anselmino, S. Melis) modified by colour factors Follows general line of factorization – all UV to hard part. Also a way to QCD evolution (cf talks of I. Cherednikov, L. Gamberg)?!

What is “Leading” twist? Practical Definition - Not suppressed as M/Q However – More general definition: Twist 3 may be suppresses as M/P T .Twist 3 may contribute at leading order in 1/Q ! Does this happen indeed?? – Explicit calculation for the case when Q >> P T

Final Pion -> Photon: SIDIS -> SIDVCS (clean, easier than exclusive) - analog of DVCS

Twist 3 partonic subprocesses for SIDVCS

Real and virtual photons - most clean tests of QCD Both initial and final – real :Efremov, O.T. (85) Initial – quark/gluon, final - real : Efremov, OT (86, fermionic poles); Qui, Sterman (91, GLUONIC poles) Initial - real, final-virtual (or quark/gluon) – Korotkiian, O.T. (94) Initial –virtual, final-real: O.T., Srednyak (05; smooth transition from fermionic via hard to GLUONIC poles).

Quark-gluon correlators Non-perturbative NUCLEON structure – physically mean the quark scattering in external gluon field of the HADRON. Depend on TWO parton momentum fractions For small transverse momenta – quark momentum fractions are close to each other- gluonic pole; probed if : Q >> P T>> M

Cross-sections at low transverse momenta: (14) - non-suppressed for large Q if Gluonic pole exists=effective Sivers function; spin-dependent looks like unpolarized (soft gluon)

Other way - NP Sivers and gluonic poles at large PT (P. G Other way - NP Sivers and gluonic poles at large PT (P.G. Ratcliffe, OT, hep-ph/0703293 ) Sivers factorized (general!) expression Expand in kT = twist 3 part of Sivers

From Sivers to twist 3 - II Angular average : As a result M in numerator - sign of twist 3. Higher moments – higher twists. KT dependent function – resummation of higher twists

From Sivers to gluonic poles - III Final step – kinematical identity Two terms are combined to one Key observation – exactly the form of Master Formula for gluonic poles (Koike et al, 2007)

Effective Sivers function Follows the expression similar to BMP Up to Colour Factors ! Defined by colour correlation between partons in hadron participating in (I)FSI SIDIS = +1; DY= -1: Collins sign rule Generally more complicated Factorization in terms of twist 3 but NOT SF

Colour correlations SIDIS at large pT : -1/6 for mesons from quark, 3/2 from gluon fragmentation (kaons?) DY at large pT: 1/6 in quark antiquark annihilation, - 3/2 in gluon Compton subprocess – Collins sign rule more elaborate – involve crossing of distributions and fragmentations - special role of PION DY (COMPASS). Direct inclusive photons in pp = – 3/2 Hadronic pion production – more complicated – studied for P-exponentials by Amsterdam group + VW IF cancellation – small EFFECTIVE SF Vary for different diagrams – modification of hard part FSI for pions from quark fragmentation -1/6 x (non-Abelian Compton) +1/8 x (Abelian Compton)

How to pass from high to low PT Hard poles in correlators (become soft at small PT – c.f. SIDVCS) Low pT – cannot distinguish fragmentation from quarks and gluons: 3/2-1/6 = 4/3 (Abelian) Strong transverse momentum dependence, very different for mesons from quark and gluon fragmentation

Colour flow Quark at large PT:-1/6 Gluon at large PT : 3/2 Low PT – combination of quark and gluon: 4/3 (absorbed to definition of Sivers function) Similarity to colour transparency phenomenon

Sivers function and formfactors Relation between Sivers and AMM known on the level of matrix elements (Brodsky, Schmidt, Burkardt) Phase? Duality for observables? Solution: SSA in DY

SSA in DY TM integrated DY with one transverse polarized beam (cf talk of S. Melis)– unique SSA – gluonic pole (Hammon, Schaefer, OT)

SSA in exclusive limit Proton-antiproton – valence annihilation - cross section is described by Dirac FF squared The same SSA due to interference of Dirac and Pauli FF’s with a phase shift Exclusive large energy limit; x -> 1 : (d/dx)T(x,x)/q(x) -> Im F2/F1 No suppression of large x – large E704 SSA Positivity: Twist 4 correction to q(x) may be important

Kinematical domains for SSA’s x Sivers PT Twist 3 FF’s

Duality between various QCD mechanisms for exclusive amplitudes (Anikin, Cherednikov, Stefanis, OT, 08) 2 pion production : GDA (small s) vs TDA+DA (small t) Scalar model - asymptotics(Efremov, Ginzburg, Radyushkin…)

Duality in scalar model “Right” (TDA, red) and “wrong” (GDA, blue) asymptotics / exact result (>1- negative “Higher Twist”

Duality in QCD Qualitatively- surprisingly good, quantitatively - model-dependent

Duality and helicity amplitudes Holds if different mechanisms contribute to SAME helicity amplitudes Scalar- only one; QCD – L and T photons Other option : Different mechanisms – different helicity amplitudes (“unmatching”) Example -> transition from perturbative phase to twist 3 (m -> M)

Twist 3 factorization (Efremov, OT ’84, Ratcliffe,Qiu,Sterman) Convolution of soft (S) and hard (T) parts Vector and axial correlators: define hard process for both double ( ) and single asymmetries

Twist 3 factorization -II Non-local operators for quark-gluon correlators Symmetry properties (from T-invariance)

Twist-3 factorization -III Singularities Very different: for axial – Wandzura-Wilczek term due to intrinsic transverse momentum For vector-GLUONIC POLE (Qiu, Sterman ’91) – large distance background

Sum rules EOM + n-independence (GI+rotational invariance) –relation to (genuine twist 3) DIS structure functions

Sum rules -II To simplify – low moments Especially simple – if only gluonic pole kept:

Gluonic poles and Sivers function Gluonic poles – effective Sivers functions-Hard and Soft parts talk, but SOFTLY Implies the sum rule for effective Sivers function (soft=gluonic pole dominance assumed in the whole allowed x’s region of quark-gluon correlator)

Compatibility of SSA and DIS Extractions of and modeling of Sivers function: – “mirror” u and d Second moment at % level Twist -3 - similar for neutron and proton and of the same sign – no mirror picture seen –but supported by colour ordering! Scale of Sivers function reasonable, but flavor dependence differs qualitatively. Inclusion of pp data, global analysis including gluonic (=Sivers) and fermionic poles HERMES, RHIC, E704 –like phonons and rotons in liquid helium; small moment and large E704 SSA imply oscillations JLAB –measure SF and g2 in the same run

CONCLUSIONS 3rd way from SF to GP – proof of Torino recipe supplemented by colour correlations Effective SF – small in pp - factorization in terms of twist 3 only Large x – E704 region - relation between SF, GP and time-like FF’s

Outlook (high energies) TMD vs UGPD T-odd UGPD? T-odd (P/O) diffractive distribiutions (analogs - also at small energies) Quark-hadron duality: description of gluon coupling to “exotic” objects in diffractive production via their decay widths

Relation of Sivers function to GPDs Qualitatively similar to Anomalous Magnetic Moment (Brodsky et al) Quantification : weighted TM moment of Sivers PROPORTIONAL to GPD E (hep-ph/0612205 ): Burkardt SR for Sivers functions is now related to Ji SR for E and, in turn, to Equivalence Principle

How gravity is coupled to nucleons? Current or constituent quark masses ?– neither! Energy momentum tensor - like electromagnertic current describes the coupling to photons

Equivalence principle Newtonian – “Falling elevator” – well known and checked Post-Newtonian – gravity action on SPIN – known since 1962 (Kobzarev and Okun’) – not yet checked Anomalous gravitomagnetic moment iz ZERO or Classical and QUANTUM rotators behave in the SAME way

Gravitational formfactors Conservation laws - zero Anomalous Gravitomagnetic Moment : (g=2) May be extracted from high-energy experiments/NPQCD calculations Describe the partition of angular momentum between quarks and gluons Describe interaction with both classical and TeV gravity – similar t-dependence to EM FF

Electromagnetism vs Gravity Interaction – field vs metric deviation Static limit Mass as charge – equivalence principle

Gravitomagnetism Gravitomagnetic field – action on spin – ½ from spin dragging twice smaller than EM Lorentz force – similar to EM case: factor ½ cancelled with 2 from Larmor frequency same as EM Orbital and Spin momenta dragging – the same - Equivalence principle

Sivers function and Extended Equivalence principle Second moment of E – zero SEPARATELY for quarks and gluons –only in QCD beyond PT (OT, 2001) - supported by lattice simulations etc.. -> Gluon Sivers function is small! (COMPASS, STAR, Brodsky&Gardner) BUT: gluon orbital momentum is NOT small: total – about 1/2, if small spin – large (longitudinal) orbital momentum Gluon Sivers function should result from twist 3 correlator of 3 gluons: remains to be proved!

Generalization of Equivalence principle Various arguments: AGM 0 separately for quarks and gluons – most clear from the lattice (LHPC/SESAM, confirmed recently)

CONCLUSIONS Sivers and other TMD functions contain infinite tower of twists starting from 3 – special role of moments Colour charge of initial/final partons crucial – NO factorization in naive sense Transverse momentum dependence of Sivers SSA in SIDIS and DY (PAX) is a new sensitive test of QCD Relation of Sivers function to twist 3 in DIS: Reasonable magnitude, but problems with flavor dependence.Bochum results with suppressed singlet twist 3 supported! Relation of Sivers to GPD’s – link to Nucleon Spin and Equivalence Principle Problems: evolution (no WW for Sivers) and SR from twist 3.